BACKGROUND
[0001] The invention relates generally to an electric power grid and more specifically to
control of capacitor bank switching in the power grid.
[0002] The basic structure of an electric power system comprises various hardware elements
such as generators, transformers, and real-time monitoring equipment, and software
such as power flow analysis software, fault detection software, and restoration software
for generation, transmission, and distribution of electricity.
[0003] In general, power system operators ensure the quality of the power supplied to the
customers by maintaining the load bus voltages within their permissible limits. Any
changes to the system configuration or in power demands can result in higher or lower
voltages in the system. This situation can be improved by reallocating the reactive
power generated in the system by adjusting transformer taps, changing generator voltages,
and by switching VAR sources such as capacitor banks or static VAR compensators (SVCs).
[0004] Capacitor banks in the power grid are often used to provide leading reactive power
compensation or power factor correction. The use of capacitor banks has increased
because they are relatively inexpensive, easy and quick to install, and can be deployed
virtually anywhere in the network. Capacitor bank installation has other beneficial
effects on the system such as: improvement of the voltage at the load, better voltage
regulation, reduction of losses, and reduction or postponement of investments in transmission.
[0005] Optimizing capacitor bank switching helps electric delivery companies minimize the
cost of installing and maintaining equipment on a distribution feeder and achieve
better performance from the available capacitor banks. There are various algorithms
available for optimizing capacitor bank switching. However, most of these algorithms
are combined with voltage control algorithms and thus lead to long convergence times.
Further most of these algorithms result in certain capacitor banks being switched
on and off more times in a day than desired. Frequent switching of capacitor banks
degrades switching contacts of the capacitor banks and increases maintenance requirements
and decreases lifetime.
[0006] Therefore, there is a need for an improved optimization approach to capacitor bank
switching.
BRIEF DESCRIPTION
[0007] In accordance with an embodiment of the present invention, a method of operating
capacitor banks in a power grid is provided. The method includes obtaining a reactive
power shortage curve forecast for a time period and generating at least one capacitor
bank power schedule curve to supply reactive power to the power grid during the time
period. The method further includes updating the at least one capacitor bank power
schedule curve to generate an optimized capacitor bank power schedule curve for reducing
the area between the reactive power shortage curve and the capacitor bank power schedule
curve. The method further includes providing switching signal commands for operating
capacitor banks based on the optimized capacitor bank power schedule curve.
[0008] In accordance with another embodiment of the present invention a power grid system
including a plurality of capacitor banks and a capacitor bank switching system is
provided. The capacitor bank switching system includes a load forecast module to obtain
a reactive power shortage curve for a time period and a capacitor bank scheduling
module for generating at least one capacitor bank power schedule curve to supply reactive
power to the power grid during the time period. The capacitor bank switching system
also includes an optimization module to update the at least one capacitor bank power
schedule curve and generate an optimized capacitor bank power schedule curve to reduce
the area between the reactive power shortage curve and the capacitor bank power schedule
curve. The capacitor bank switching system further includes a control circuitry to
provide switching signal commands for operating capacitor banks based on the optimized
capacitor bank power schedule.
[0009] In accordance with yet another embodiment of the present invention, a computer-readable
medium comprising non-transitory computer-readable instructions of a computer program
that, when executed by a processor, cause the processor to perform a method of operating
capacitor banks in a power grid is provided. The method includes obtaining a reactive
power shortage curve forecast for a time period and generating at least one capacitor
bank power schedule curve to supply reactive power to the power grid during the time
period. The method further includes updating the at least one capacitor bank power
schedule curve to generate an optimized capacitor bank power schedule curve for reducing
the area between the reactive power shortage curve and the capacitor bank power schedule
curve. The method further includes providing switching signal commands for operating
capacitor banks based on the optimized capacitor bank power schedule curve.
DRAWINGS
[0010] These and other features, aspects, and advantages of the present invention will become
better understood when the following detailed description is read with reference to
the accompanying drawings in which like characters represent like parts throughout
the drawings, wherein:
FIG. 1 is a diagrammatical representation of an overall electric system;
FIG. 2 is a diagrammatical representation of a capacitor bank and a capacitor unit;
FIG. 3 is a flow chart representing a method of operating capacitor banks in a power
grid in accordance with an embodiment of the present invention;
FIG. 4 is a graphical representation of under-coverage and over-coverage capacitor
bank power schedule curves; and
FIG. 5 is a graphical representation describing a branch and bound optimization method
in accordance with an embodiment of the present invention.
DETAILED DESCRIPTION
[0011] FIG. 1 illustrates a single line diagram of an overall electric system 10 from generation
to utilization. The electric system 10 includes a generating station 12, a transmission
substation 14, local substations or distribution substations 16 and loads 18. Generating
station 12 may comprise a hydropower generating station, a thermal power generating
station, a wind power generating station, or a solar power generating station, for
example. Generating station 12 generates electricity at a generating station voltage
which is typically in the range of 4 kV to 13 kV. The generating station voltage is
stepped up to a higher transmission level voltage such as 110 kV and above by a generating
station transformer (not shown) for more efficient transfer of the electricity.
[0012] The electricity at the transmission level voltage is transmitted to transmission
substation 14 by primary transmission lines 20 that are configured to carry electricity
long distances. At transmission substation 14, a reduction in voltage occurs for distribution
to other points in the system through secondary transmission lines 22. Further voltage
reductions for commercial and industrial or residential loads 18 may occur at distribution
substation 16. The distribution substation 16 may supply electricity at voltages in
the range of 4 kV to 69 kV, for example. The voltages may further by reduced by one
or two more levels at distribution substation 16 or other local substations (not shown)
receiving power from distribution substation 16 to supply the electricity to residential
loads at lower voltages such as 120 V or 240 V. Capacitor banks (not shown) may be
placed anywhere in the system such as at the transmission substation or distribution
substation, for example.
[0013] A utility control center 24 is used in the system 10 for operation and maintenance
of generating station 12, transmission substation 14, and distribution substations
16. Utility control center 24 receives data from these components and also provides
control signals to these components. Loads 18 may communicate with their respective
distribution substations 16 and thus the utility control center 24 may also receive
and transmit information to and from the loads 18. Components of the utility control
center 24 include a supervisory control and data acquisition (SCADA) system 26, an
energy management system (EMS) 28, a demand response management system (DRMS) 30,
and a distribution management system (DMS) 32. In one embodiment, some of these components
may be provided separately in system 10 rather than being integrated in the utility
control center 24.
[0014] As will be appreciated by those skilled in the art, SCADA usually refers to basic
control and monitoring of field devices including breakers, switches, capacitors,
reclosers, and transformers. EMS 28 coordinates and optimizes power generation and
transmission, whereas DMS 32 coordinates power distribution. EMS 28 and DMS 32 include
applications such as automatic generation control (AGC), load forecasting, capacitor
bank switching controls, engineering load flow modeling, economic dispatch, energy
accounting, interchange transactions, reserve calculations (spin and non-spin), and
VAR/voltage control. DRMS 30 controls peak demand and produces other economies without
major inconvenience to the customer. In some embodiments, DRMS 30 is added as a function
of the EMS 28 because of its use in controlling overall peak demand and generation
requirements. Further DMS 32 includes functions and capabilities that may improve
the reliability and efficiency of the power distribution system.
[0015] Fig. 2 shows a capacitor unit 110 which is a building block of a capacitor bank 120.
Capacitor bank 120 is configured using one or more series groups of parallel connected
capacitor units 110 per phase. Capacitor unit 110 is made up of individual capacitor
elements 112, arranged in parallel/ series connected groups, within a steel enclosure
114. In one embodiment an internal discharge device 116 in capacitor unit 110 is used
when needed to reduce residual voltage. For example, an appropriately sized resistor
may be used for reducing the unit residual voltage by 50 V or less in 5 minutes. Capacitor
units 110 are available in a variety of voltage ratings, typically 240 V to 24940V,
and sizes 2.5 kvar to about 1000 kvar, for example.
[0016] Fig. 3 shows a method 50 of operating capacitor banks in the power grid in accordance
with an embodiment of the present invention. The method may be employed by the DMS
32 or EMS 28 (FIG. 1), for example, and includes obtaining a forecast for reactive
power shortage in step 52. The reactive power shortage forecast may be obtained by
subtracting total reactive power being generated by reactive power sources from the
total reactive power demand for a time period or period of interest based on a desired
power factor. In one embodiment, the reactive power sources may include capacitor
banks that are already connected to the system. The reactive power forecast may be
determined in terms of MVA loading which is indicative of active as well as reactive
power for a particular zone. In one embodiment, the period of interest may be an hour,
a day, a week, or any other suitable time determined by the user or the operator.
In another embodiment, the reactive power forecast is determined for k time steps
into the future, where k is again a number determined by the operator. As will be
appreciated by those skilled in the art, reactive power forecasting methods may include
similar day approaches, various regression models, time series approaches, neural
networks, expert systems, fuzzy logic, and statistical learning algorithms.
[0017] In step 54, at least one capacitor bank power schedule curve may be generated to
supply power to the power grid during the period of interest. In one example, the
at least one capacitor bank power schedule curve may comprise a curve representative
of reactive from scheduling of a single capacitor bank. For example, if a capacitor
bank with a rating of 100 kVAr is scheduled to operate from morning 8 to 11 then the
capacitor bank power schedule curve will be a rectangle with amplitude of 100 kVAr
for that period. In a given zone there may be a number of capacitor banks having similar
and/or different ratings. Thus, in such a scenario, the capacitor bank power schedule
curve refers to a power curve obtained from the reactive power generated by the capacitor
banks as the capacitor banks are switched on in accordance with the switching schedule.
Since there are a numbers of capacitor banks, the capacitor banks may be switched
in multiple different combinations for the period of interest resulting into a plurality
of potential capacitor bank power schedule curves. Thus, in step 54 all such capacitor
bank power schedule curves of different combinations of capacitor banks may be determined.
The capacitor bank power schedule curve may either be an under-coverage curve or an
over-coverage curve. In an under-coverage curve, the limits of the capacitor bank
power schedule curve are within the reactive power shortage curve, whereas, in an
over-coverage curve, the limits of the capacitor bank power schedule curve are outside
of the reactive power shortage curve. FIG. 4 describes under-coverage and over-coverage
curves in more detail.
[0018] In step 56, the at least one capacitor bank power schedule curve is updated to generate
an optimized capacitor bank power schedule curve for reducing or minimizing the area
between the reactive power shortage curve and the capacitor bank power schedule curve.
Updating the at least one capacitor bank power schedule curve includes adding more
capacitor banks into the system at different times. Optimization techniques such as
dynamic programming, a greedy algorithm, or a branch and bound algorithm may be employed
to determine the optimized capacitor bank power schedule curve. Reducing the area
between the reactive power shortage curve and the capacitor bank power schedule curve
has been found to result in reactive power compensation being achievable with less
capacitor bank switching events as compared with convention capacitor bank control
embodiments. For example, rather than switching a particular capacitor bank 7-8 times
during the time period, the optimization technique may result in switching the capacitor
bank only once or twice throughout the time period. Once the optimized capacitor bank
power schedule curve is determined, the information may be utilized in step 58 for
operating the capacitor banks by providing appropriate switching signal commands to
the capacitor banks.
[0019] FIG. 4 shows graphical illustrations 70, 80 of under-coverage and over-coverage capacitor
bank power schedule curves respectively. In both plots 70, 80, a reactive power shortage
curve is shown by curve 72. In plot 70, two capacitor banks are used to supply the
reactive power demand over a period of time whereas in plot 80, three capacitor banks
are used as shown. Further, in plot 70, a capacitor bank power curve 74 generated
by two capacitor banks is within the bounds of reactive power shortage curve 72 and
is hence an under-coverage curve, whereas in plot 80 a capacitor bank power curve
82 is outside of the limits of reactive power shortage curve 72 and hence represents
an over-coverage curve.
[0020] To describe under coverage curve in more detail, capacitor bank curve 74 is generated
with two capacitor banks supplying reactive power from time
w to
z. A first capacitor bank CB1 of rating p kVAr is switched on from time
w to
z whereas, a second capacitor bank CB2 of rating
q kVAr is switched on from time x to y which is shorter than the time
w to
z. Thus, the resultant capacitor bank curve 74 has an amplitude of
p kVAr from time w to
x and
y to
z when it is operating alone whereas the amplitude goes up to
p+q kVAr from time
x to
y when both capacitor banks are supplying reactive power to the grid.
[0021] FIG. 5 describes a branch and bound optimization method 90 of minimizing the area
between the reactive power shortage curve and the capacitor bank power schedule curve
with reduced capacitor banks switchings. The branch-and-bound (BB) method is based
on the idea of intelligently enumerating all the feasible points of a combinatorial
optimization problem. As will be appreciated by those skilled in the art, in BB method,
we try to construct a proof that a solution is optimal based on successive partitioning
of the solution space. The branch in BB corresponds to the partitioning process, and
the bound refers to the lower bounds that are used to construct a proof of optimality
without exhaustive search. For this particular example assume that there is a set
of four capacitor banks (CBs) in a particular zone, CB1 with capacity of 200 kVAr,
CB 2 with 200 kVAr, CB3 with 60 kVAr and CB4 again with 200 kVAr respectively. The
circles in Fig. 5 correspond to subsets of CBs. The circle at the top in step 92 is
the starting point, the empty subset (i.e., No CBs). At each step, the selected circle
is labeled as parent and its children are found by adding one CB at a time that has
not been in the subset yet. Further, at each step a number of subsets are selected
for further investigation into the next step. The subsets selected (represented by
the circles that are not crossed out) depend on their cost and beam width. The beam
width here refers to the number of branches which are selected by the operator and
is part of bounding the algorithm. The cost is generally a representation of area
difference between the reactive power shortage curve and the capacitor bank power
schedule curve. For example, the more the area difference, the higher the cost.
[0022] Step 94 of FIG. 5, shows four subsets with only one parent CB (CB1 or CB2 or CB3
or CB4) i.e., only one capacitor bank is supplying power to the grid for a particular
period of time. In step 94, only a pre-defined number of these ordered subsets are
selected. In one embodiment, only the subsets with minimal costs are selected. In
the example shown, the beam width selected is 2. Thus, at each step only 2 subsets
are selected and the cost of the ordered subset at each step is determined. Bounding
the number of branches off the parent CB based on the beam width decreases the complexity
of the algorithm compared to a more exhaustive search. However, such bounding may
leads to a suboptimal solution. The optimality of the solution increases with the
increased beam width. Thus, the operator selects the beam width based on the optimal
solution requirement.
[0023] For determining the cost of the ordered subset, the following equation may be used.
wherein A is the area under the reactive power shortage curve, D is the total number
of capacitor banks in the subset, and
pi is the profit or actual reactive power supplied by an
ith capacitor bank over a certain period of time. In one embodiment, the profit
pi of a capacitor bank can be determined by following equation:
wherein
wi is the weight or capacity of the
ith capacitor bank, and
li is the length or the time duration for which the capacitor bank may be switched on
to supply the reactive power to the grid during reactive power shortage. The length
li is calculated by finding points in time where the cumulative reactive power supplied
by the
ith CB and CBs prior to
ith CB in schedule is lower than the reactive power shortage curve.
[0024] For example, in the embodiment of FIG. 5, in step 94 it is first determined which
of the subsets 1 (CB1), 2 (CB2), 3 (CB3) and 4 (CB4) have lower costs. If the peak
reactive power shortage curve is a parabolic curve with peak of 660 kVAr, then the
cost of subset 1, 2, and 4 may be lower compared any combination including subset
3. Thus, subset 3 is discarded due to its high cost. Further, since the beam width
is 2, even though subset 4 has similar cost as that of subset 1 and subset 2, it is
discarded too. Referring back to FIG. 4, subset 1 is selected means at first level
CB1 is assumed to be operated from a time period
w to
z.
[0025] Now the step 96 has two subsets with two starting capacitor banks CB1 and CB2 respectively.
With respect to the subset starting with capacitor bank CB1 in step 96, remaining
capacitor banks CB2, CB3 and CB4 are added to that subset for updating the capacitor
bank scheduling curve. The cost of each of these combinations or updated curves (i.e.,
CB1 + CB2 or CB1 + CB3, or CB1 + CB4) is again determined and the lowest cost combination
or combinations are selected as subsets for further calculations in step 98 with beam
width of 2. As can be seen from FIG. 5, CB2 and CB 4 are added to the two different
subsets or branches respectively. Similar calculations and branching (not shown) may
also be done for the subset starting with CB2 in Step 94. Cost calculation and updating
the subset with more capacitor banks to reduce the cost is repeated in steps 98 and
100 until the desired reactive power is met. Again referring back to FIG. 4, it can
be seen that at level 2, capacitor bank CB2 is added to CB1 from time period x to
y to increase the total reactive power to
p+
q kVAr and minimize the area between reactive power shortage curve and capacitor bank
reactive power curve. The steps are repeated until one is short of number capacitor
banks or the area difference achieved is minimum.
[0026] The above description of BB algorithm takes into account the under-coverage curve.
For the over-coverage curve, the method is similar to the under-coverage curve algorithm
except that the optimization problem is formulated to minimize the difference between
the area covered by CBs and the shortage curve instead of the difference between the
shortage curve and CBs and the length is calculated based on mechanisms similar to
those of under-coverage curve.
[0027] In certain embodiments, it may be necessary to divide the reactive power shortage
curve in multiple curves of small durations. For example, rather than having a single
24 hour curve, the curve may be split into 6 curves of 4 hours each, and the above
algorithm may then be employed on each of the curves separately. In such situations
it is helpful to calculate the number of capacitor bank switching events, i.e., how
many times a capacitor bank is being switched on and off and to restrict the number
of events per time period to a number decided by the operator. This may be necessary
because capacitor bank lifetime depends on the number of switching events per day.
[0028] While only certain features of the invention have been illustrated and described
herein, many modifications and changes will occur to those skilled in the art. It
is, therefore, to be understood that the appended claims are intended to cover all
such modifications and changes as fall within the scope of the invention as defined
in the accompanying claims.
1. A method (50) for operating capacitor banks in a power grid comprising:
obtaining (52) a reactive power shortage curve forecast for a time period;
generating (54) at least one capacitor bank power schedule curve to supply reactive
power to the power grid during the time period;
updating (56) the at least one capacitor bank power schedule curve to generate an
optimized capacitor bank power schedule curve for reducing the area between the reactive
power shortage curve and the capacitor bank power schedule curve; and
providing (58) switching signal commands for operating capacitor banks based on the
optimized capacitor bank power schedule curve.
2. The method of claim 1, wherein obtaining (52) the reactive power shortage curve forecast
comprises utilizing at least one of a regression algorithm, a time series algorithm,
a neutral network algorithm, a fuzzy logic algorithm or a statistical learning algorithm.
3. The method of claim 1 or claim 2, wherein updating the at least one capacitor bank
power schedule curve comprises utilizing an optimization technique to optimize the
capacitor bank power schedule curve.
4. The method of claim 3, wherein the optimization technique comprises a dynamic programming
algorithm, a greedy algorithm or a branch and bound (BB) algorithm.
5. The method of claim 4, wherein the branch and bound (BB) algorithm comprises identifying
at least one least cost capacitor bank subset.
6. The method of claim 5, wherein the identifying at least one least cost capacitor bank
subset comprises: updating the at least one capacitor bank subset by adding child
capacitor banks to parent capacitor banks; and/or is based on an area difference between
the reactive power shortage curve and the capacitor bank power schedule curve, and/or
constraining a capacitor bank subset based on a beam width.
7. The method of any one of claims 1 to 6, wherein the capacitor bank power schedule
curve comprises an under-coverage curve or an over-coverage curve.
8. The method of claim 10, wherein, when the capacitor bank scheduling curve comprises
under-coverage curve, the BB algorithm: reduces the difference between the reactive
power shortage curve and the capacitor bank scheduling curve, or reduces the difference
between the capacitor bank scheduling curve and the reactive power shortage curve.
9. The method of claim 1 further comprising dividing the reactive power shortage curve
in multiple curves of small durations during the time period, or wherein preferably
a number of switching signal commands for at least one capacitor bank during the time
period are restricted.
10. A computer-readable medium comprising non-transitory computer-readable instructions
of a computer program that, when executed by a processor, cause the processor to perform
the method (50) of operating capacitor banks in a power grid of any one of claims
1 to 9.
11. A power grid system comprising:
a plurality of capacitor banks (120);
a capacitor bank switching system (50) comprising:
a load forecast module (52) to obtain a reactive power shortage curve for a time period;
a capacitor bank scheduling module (54) for generating at least one capacitor bank
power schedule curve to supply reactive power to the power grid during the time period;
an optimization module (56) for updating the at least one capacitor bank power schedule
curve and generating an optimized capacitor bank power schedule curve to reduce the
area between the reactive power shortage curve and the capacitor bank power schedule
curve; and
a control circuitry (58) for providing switching signal commands for operating capacitor
banks based on the optimized capacitor bank power schedule.
12. The power grid system of claim 11, wherein the optimization module (56) comprises
an optimization technique to optimize the capacitor bank power schedule curve.
13. The power grid system of claim 12, wherein the optimization technique comprises a
dynamic programming algorithm, a greedy algorithm or a branch and bound (BB) algorithm.
14. The power grid system of any one of claims 11 to 13, wherein the branch and bound
(BB) algorithm identifies at least one least cost capacitor bank subset.
15. The power grid system of claim 14, wherein at least one least cost capacitor bank
subset is identified based on an area difference between the reactive power shortage
curve and the capacitor bank power schedule curve.